Simplify the following expression: $\dfrac{80r}{8r^3}$ You can assume $r \neq 0$.
$ \dfrac{80r}{8r^3} = \dfrac{80}{8} \cdot \dfrac{r}{r^3} $ To simplify $\frac{80}{8}$ , find the greatest common factor (GCD) of $80$ and $8$ $80 = 2 \cdot 2 \cdot 2 \cdot 2 \cdot 5$ $8 = 2 \cdot 2 \cdot 2$ $ \mbox{GCD}(80, 8) = 2 \cdot 2 \cdot 2 = 8 $ $ \dfrac{80}{8} \cdot \dfrac{r}{r^3} = \dfrac{8 \cdot 10}{8 \cdot 1} \cdot \dfrac{r}{r^3} $ $\phantom{ \dfrac{80}{8} \cdot \dfrac{1}{3}} = 10 \cdot \dfrac{r}{r^3} $ $ \dfrac{r}{r^3} = \dfrac{r}{r \cdot r \cdot r} = \dfrac{1}{r^2} $ $ 10 \cdot \dfrac{1}{r^2} = \dfrac{10}{r^2} $